Torres has been woefully out of form since joining Chelsea for £50m in January but got the nod to start the Champions League quarter-final second leg.
He was subsequently hauled off at half-time for Drogba, who dragged the Blues back into the tie with a well taken goal before United sealed a 2-1 win on the night and 3-1 aggregate victory.
And May reckons the result could have been a lot different had Drogba played from the start, telling the Alan Brazil Sports Breakfast: “When I saw the teamsheet I was delighted, once I saw Drogba on the bench.
“Fernando Torres is a fantastic striker and it will change for him I’m sure but when you’re in such a bad run of form as he is then you’ve got to play people who can do it week in week out.”
United remain course for the treble and May reckons Nemanja Vidic is the main reason behind the club’s success this season.
He added: “One person that’s stood out for Man United this season and probably for the last four or five years is Nemanja Vidic.
"The manager has given him the captaincy and rightly so. He is of the two or three best centre-halves in the country definitely and probably in Europe."
And May has backed the Reds to secure a place in the FA Cup final this weekend by beating rivals Manchester City.
"United have got the momentum now and the way they are playing I just can't see them getting beat on Saturday," he said.